Lattice gauge theories with fermions in multiple representations (“multirep” theories) provide an arena to test the old
ideas of tumbling or (for vectorlike systems) scale separation [1]}.
The physical picture is that when a gauge coupling becomes sufficiently strong in the
infrared, a scalar fermion bilinear will form, breaking chiral symmetry.
In a system with multiple representations of fermions, a weaker gauge coupling is needed to drive
condensation for higher representation fermions, since their color charges are greater.
Thus, different representations of fermion may condense at different scales.
Quenched simulations from the early 80's (performed on small lattices with large gauge couplings)
[2]}, [3]}, [4]}, [5]}
appeared to show such behavior. However, quenching neglects the back-reaction of the fermions
on the gauge dynamics.
It may also happen that the scales for chiral symmetry breaking and deconfinement are different.
Some old simulations with dynamical fermions (see [6]})
indicate this behavior. The issue with these systems is that they all
appear to be near or beyond the conformal window (whose precise boundary is still controversial), so they may not be chirally broken at all.
(See refs. [7]}, [8]} for reviews.)
